{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZNS23CT3A4SPDWTYCOYUDU2F7Z","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bf97e5a8922e733dab54c64495564cdf54cf4fb1cde89691b24ff1fdfee0b13f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-08-11T14:07:06Z","title_canon_sha256":"bb149ea88424370323e87c6916c69417ff708191f21c1dfd5ffa062eb3664331"},"schema_version":"1.0","source":{"id":"0908.1505","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1505","created_at":"2026-05-18T04:37:22Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1505v2","created_at":"2026-05-18T04:37:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1505","created_at":"2026-05-18T04:37:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZNS23CT3A4SP","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZNS23CT3A4SPDWTY","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZNS23CT3","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:fdc4050e0ab281f199c18cdc623f8a8f7d29656df7bc8e3cc7ffd2c18d6a0ff6","target":"graph","created_at":"2026-05-18T04:37:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"There is a natural one-to-one correspondence between squarefree monomial ideals and finite simple hypergraphs via the cover ideal construction. Let H be a finite simple hypergraph, and let J = J(H) be its cover ideal in a polynomial ring R. We give an explicit description of all associated primes of R/J^s, for any power J^s of J, in terms of the coloring properties of hypergraphs arising from H. We also give an algebraic method for determining the chromatic number of H, proving that it is equivalent to a monomial ideal membership problem involving powers of J. Our work yields two new purely al","authors_text":"Adam Van Tuyl, Christopher A. Francisco, Huy Tai Ha","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-08-11T14:07:06Z","title":"Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1505","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1147de8ed51ba3d70a5bb443a9e79ee673e56d367ef4f51b684df67936f3bc36","target":"record","created_at":"2026-05-18T04:37:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bf97e5a8922e733dab54c64495564cdf54cf4fb1cde89691b24ff1fdfee0b13f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-08-11T14:07:06Z","title_canon_sha256":"bb149ea88424370323e87c6916c69417ff708191f21c1dfd5ffa062eb3664331"},"schema_version":"1.0","source":{"id":"0908.1505","kind":"arxiv","version":2}},"canonical_sha256":"cb65ad8a7b0724f1da7813b141d345fe430c9fb040bb3e9d6e0b962d4e5fca2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb65ad8a7b0724f1da7813b141d345fe430c9fb040bb3e9d6e0b962d4e5fca2d","first_computed_at":"2026-05-18T04:37:22.296693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:22.296693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t798QSyFMpNN9xMuH+Et/XbmGEZfAp5qK5k2mCSWjrW6LivqPg2IBx3TROIOf8XPmqzgcW4qJ/gRiqJx1Dp/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:22.297265Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.1505","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1147de8ed51ba3d70a5bb443a9e79ee673e56d367ef4f51b684df67936f3bc36","sha256:fdc4050e0ab281f199c18cdc623f8a8f7d29656df7bc8e3cc7ffd2c18d6a0ff6"],"state_sha256":"e2b1679eaa5ec7dd07fb221a2e0043f13ea4013ffbad3595cf063e13cf44c58f"}